Question

A light string passing over a smooth light fixed pulley connects two blocks of masses m1 and m2. If the acceleration of the system is g/8, then the ratio of masses is

• A. \(\frac{9}{7}\)
• B. \(\frac{8}{1}\)
• C. \(\frac{4}{3}\)
• D. \(\frac{5}{3}\)

Answer 1

The Correct Option is A

The ratio of masses \( m_1 \) and \( m_2 \) is determined using principles of mechanics applied to pulley and block systems.

Given parameters:

• Masses: \( m_1 \) and \( m_2 \)
• System acceleration: \( a = \frac{g}{8} \)
• Gravitational acceleration: \( g \)

Forces acting on each mass are analyzed:

• For mass \( m_1 \):
  • Forces include string tension \( T \) and gravitational force \( m_1g \).
  • Force balance equation: \( T = m_1g - m_1a \)
• For mass \( m_2 \):
  • Forces include string tension \( T \) and gravitational force \( m_2g \).
  • Force balance equation: \( T = m_2g + m_2a \)

Equating the expressions for tension \( T \):

\(m_1g - m_1a = m_2g + m_2a\)

Substitute \( a = \frac{g}{8} \):

\(m_1g - m_1\left(\frac{g}{8}\right) = m_2g + m_2\left(\frac{g}{8}\right)\)

Simplify the equation:

\(m_1g\left(1 - \frac{1}{8}\right) = m_2g\left(1 + \frac{1}{8}\right)\)

\(\frac{7m_1g}{8} = \frac{9m_2g}{8}\)

Cancel \( g \) and simplify:

\(7m_1 = 9m_2\)

The mass ratio is therefore:

\(\frac{m_1}{m_2} = \frac{9}{7}\)

The definitive ratio is \(\frac{9}{7}\).